Question: Kevin is 2 times as old as William. 25 years ago, Kevin was 7 times as old as William. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and William. Let Kevin's current age be $k$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $k = 2w$ 25 years ago, Kevin was $k - 25$ years old, and William was $w - 25$ years old. The information in the second sentence can be expressed in the following equation: $k - 25 = 7(w - 25)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = k / 2$ . Substituting this into our second equation, we get: $k - 25 = 7($ $(k / 2)$ $- 25)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 25 = \dfrac{7}{2} k - 175$ Solving for $k$ , we get: $\dfrac{5}{2} k = 150$ $k = \dfrac{2}{5} \cdot 150 = 60$.